Function rkf, Function rkf ,16-67 – HP 50g Graphing Calculator User Manual

Page 544

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Page 16-67

Note: The option

Stiff

is also available for graphical solutions of differential

equations.

Numerical solution to ODEs with the SOLVE/DIFF menu

The SOLVE soft menu is activated by using 74 MENU in RPN mode. This menu
is presented in detail in Chapter 6. One of the sub-menus, DIFF, contains
functions for the numerical solution of ordinary differential equations for use in
programming. These functions are described next using RPN mode and system
flag 117 set to SOFT menus. (See note in page 16-75).
The functions provided by the SOLVE/DIFF menu are the following:

Function RKF

This function is used to compute the solution to an initial value problem for a
first-order differential equation using the Runge-Kutta-Fehlbert 4

th

-5

th

order

solution scheme. Suppose that the differential equation to be solved is given by
dy/dx = f(x,y), with y = 0 at x = 0, and that you will allow a convergence
criteria

ε for the solution. You can also specify an increment in the independent

variable,

Δx, to be used by the function. To run this function you will prepare

your stack as follows:

3: {‘x’, ‘y’, ‘f(x,y)’}
2: {

ε Δx }

1: x

final

The value in the first stack level is the value of the independent variable where
you want to find your solution, i.e., you want to find, y

final

= f

s

(x

final

), where f

s

(x)

represents the solution to the differential equation. The second stack level may
contain only the value of

ε, and the step Δx will be taken as a small default

value. After running function

@@RKF@@, the stack will show the lines:

2: {‘x’, ‘y’, ‘f(x,y)’}
1:

ε

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